Abstract
If $T\in \mathscr{L}(X)$ then $T$ is analytic if and only if $(\lambda-T)^{-1}$ has a pole for at least a $\lambda\in\sigma(T)$. Furthermore, every analytic operator has a non-trivial invariant subspace.
Citation
In Ho Jeon. Jin Chun Kim. Woo Young Lee. "On a spectral property of analytic operators." Tsukuba J. Math. 20 (2) 379 - 385, December 1996. https://doi.org/10.21099/tkbjm/1496163088
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